Operations Research Three Marks Questions

11th Standard

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Business Maths

Time : 00:45:00 Hrs
Total Marks : 30
    10 x 3 = 30
  1. Solve the following LPP graphically.
    Maximize \(Z=6{ x }_{ 1 }+5{ x }_{ 2 }\) Subject to the constraints \(3{ x }_{ 1 }+5{ x }_{ 2 }\le 15,\quad 5{ x }_{ 1 }+2{ x }_{ 2 }\le 10\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

  2. Solve the following LPP graphically.\(Maximize\quad Z=-{ x }_{ 1 }+2{ x }_{ 2 }\)
    Subject to the constraints \(-{ x }_{ 1 }+3{ x }_{ 2 }\le 10,\quad { x }_{ 1 }+{ x }_{ 2 }\le 6,\quad { x }_{ 1 }{ -x }_{ 2 }\le 2\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

  3. Solve the following LPP graphically. Minimize \(Z={ x }_{ 1 }-5{ x }_{ 2 }+20\)
    Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\ge 0,\quad { -x }_{ 1 }+2{ x }_{ 2 }\ge 2,\quad { x }_{ 1 }\ge 3,{ x }_{ 2 }\le 4\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

  4. Solve the following LPP graphically.  \(\\ \therefore \quad Maximize\quad Z=3{ x }_{ 1 }+4{ x }_{ 2 }\) 
    subject to the constraints \({ x }_{ 1 }+{ x }_{ 2 }\le 4\quad \quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0\)

  5. Solve the following LPP graphically. Minimize\(Z=-3{ x }_{ 1 }+4{ x }_{ 2 }\)
    Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.\)

  6. Solve the following LPP graphically, Minimize \(Z=3{ x }_{ 1 }+5{ x }_{ 2 }\)
    Subject to the constraints \({ x }_{ 1 }+3{ x }_{ 2 }\ge 3,\quad { x }_{ 1 }+{ x }_{ 2 }\ge 2\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0.\)

  7. Solve the following LPP graphically. Maximize \(Z={ x }_{ 1 }+{ x }_{ 2 }\)
    Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\le -1,{ -x }_{ 1 }+{ x }_{ 2 }\le 0\quad and\quad { x }_{ 1 }+{ x }_{ 2 }\ge 0\)

  8. Construct the network for the projects consisting of various activities and their precedence relationships are as given below:

    Immediate Predecessor A B C D E F G H I
    Activity B C D,E,F G I H J K L
  9. Construct the network for the following:

    Activity A B C D E F
    Immediate Predecessor - - - A B C
  10. Develop a network based on the following information.

    Activity A B C D B E
    Immediate Predecessor - - A C E F


     

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